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IMA Journal of Applied Mathematics Advance Access originally published online on February 24, 2009
IMA Journal of Applied Mathematics 2009 74(2):178-200; doi:10.1093/imamat/hxp003
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Synchronization in delayed Cohen–Grossberg neural networks with bounded external inputs

Chun-Hsien Li

Suh-Yuh Yang{dagger}

Department of Mathematics, National Central University, Jhongli City, Taoyuan County 32001, Taiwan

{dagger} Email: syyang{at}math.ncu.edu.tw

Received on January 19, 2006; Revision received September 26, 2008. Accepted on December 16, 2008

In this paper, we study the drive-response-type synchronization in the delayed Cohen–Grossberg neural networks with bounded external inputs. The connection time delays between neurons can be of discrete or distributed form. By using the Lyapunov functional method, we establish three criteria all independent of the time delays for ensuring the occurrence of synchronization with exponential rates. Generally speaking, we prove that the exponential synchronization occurs provided some certain weighted sum of the connection and coupling strengths with other system parameters is positive enough no matter that the connection time delay is of discrete or distributed form. Our criteria improve and extend some existing ones. Furthermore, several concrete examples are provided to show that the three criteria do not include one another. Numerical simulations are also given to demonstrate the theoretical results.

Keywords: Cohen–Grossberg neural networks; discrete time delays; distributed time delays; exponential synchronization; Lyapunov functionals.


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